Multiple Regression Mannen

*Unverified author*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Wed, 24 Dec 2008 07:06:55 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/24/t1230127764hzlpw7oqxp30dms.htm/, Retrieved Wed, 24 Dec 2008 15:09:24 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/24/t1230127764hzlpw7oqxp30dms.htm/}, year = {2008}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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54156 53661 52441 50648 48141 46127 45623 56527 60205 61321 58088 54623 53495 51824 50518 49050 47111 45264 44357 54862 57871 59070 56273 52837 51702 49447 48965 46922 46256 45200 44471 53119 55016 56641 51847 47990 45744 46390 44461 41582 40813 38096 35461 44375 46255 45610 43375 40167 40628 40590 39473 36735 36634 32806 32907 41076 42254 43215 41116 40373

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation R(1)[t] = + 56288.3446327683 -292.620589052514t + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 56288.3446327683 1239.459911 45.4136 0 0 t -292.620589052514 35.338695 -8.2805 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.736030589681346 R-squared 0.54174102894667 Adjusted R-squared 0.533840012204372 F-TEST (value) 68.5659892411583 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 2.07849293332174e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4740.52490574454 Sum Squared Residuals 1303409430.15509 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 54156 55995.7240437159 -1839.72404371591 2 53661 55703.1034546633 -2042.10345466332 3 52441 55410.4828656108 -2969.48286561081 4 50648 55117.8622765583 -4469.8622765583 5 48141 54825.2416875058 -6684.24168750578 6 46127 54532.6210984533 -8405.62109845327 7 45623 54240.0005094008 -8617.00050940076 8 56527 53947.3799203482 2579.62007965176 9 60205 53654.7593312957 6550.24066870427 10 61321 53362.1387422432 7958.86125775679 11 58088 53069.5181531907 5018.4818468093 12 54623 52776.8975641382 1846.10243586182 13 53495 52484.2769750857 1010.72302491433 14 51824 52191.6563860332 -367.656386033154 15 50518 51899.0357969806 -1381.03579698064 16 49050 51606.4152079281 -2556.41520792813 17 47111 51313.7946188756 -4202.79461887561 18 45264 51021.1740298231 -5757.1740298231 19 44357 50728.5534407706 -6371.55344077058 20 54862 50435.9328517181 4426.06714828193 21 57871 50143.3122626656 7727.68773733445 22 59070 49850.691673613 9219.30832638696 23 56273 49558.0710845605 6714.92891543948 24 52837 49265.450495508 3571.54950449199 25 51702 48972.8299064555 2729.17009354450 26 49447 48680.209317403 766.79068259702 27 48965 48387.5887283505 577.411271649534 28 46922 48094.968139298 -1172.96813929795 29 46256 47802.3475502454 -1546.34755024544 30 45200 47509.7269611929 -2309.72696119292 31 44471 47217.1063721404 -2746.10637214041 32 53119 46924.4857830879 6194.51421691211 33 55016 46631.8651940354 8384.13480596462 34 56641 46339.2446049829 10301.7553950171 35 51847 46046.6240159303 5800.37598406965 36 47990 45754.0034268778 2235.99657312216 37 45744 45461.3828378253 282.617162174678 38 46390 45168.7622487728 1221.23775122719 39 44461 44876.1416597203 -415.141659720293 40 41582 44583.5210706678 -3001.52107066778 41 40813 44290.9004816153 -3477.90048161526 42 38096 43998.2798925628 -5902.27989256275 43 35461 43705.6593035102 -8244.65930351023 44 44375 43413.0387144577 961.96128554228 45 46255 43120.4181254052 3134.58187459479 46 45610 42827.7975363527 2782.20246364731 47 43375 42535.1769473002 839.823052699823 48 40167 42242.5563582477 -2075.55635824766 49 40628 41949.9357691951 -1321.93576919515 50 40590 41657.3151801426 -1067.31518014263 51 39473 41364.6945910901 -1891.69459109012 52 36735 41072.0740020376 -4337.07400203761 53 36634 40779.4534129851 -4145.45341298509 54 32806 40486.8328239326 -7680.83282393258 55 32907 40194.2122348801 -7287.21223488006 56 41076 39901.5916458275 1174.40835417245 57 42254 39608.971056775 2645.02894322497 58 43215 39316.3504677225 3898.64953227748 59 41116 39023.72987867 2092.27012133000 60 40373 38731.1092896175 1641.89071038251 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.00457173906946854 0.00914347813893707 0.995428260930531 6 0.00132175915862471 0.00264351831724942 0.998678240841375 7 0.000294703947642487 0.000589407895284973 0.999705296052357 8 0.458478062585486 0.916956125170972 0.541521937414514 9 0.75042958656026 0.499140826879481 0.249570413439740 10 0.810418124082873 0.379163751834253 0.189581875917127 11 0.74336368780359 0.513272624392821 0.256636312196411 12 0.679682372072835 0.64063525585433 0.320317627927165 13 0.627490080912017 0.745019838175965 0.372509919087983 14 0.601438167408951 0.797123665182098 0.398561832591049 15 0.589679617573295 0.82064076485341 0.410320382426705 16 0.59793039662767 0.80413920674466 0.40206960337233 17 0.647445177752739 0.705109644494522 0.352554822247261 18 0.739402168518201 0.521195662963598 0.260597831481799 19 0.836779905223514 0.326440189552972 0.163220094776486 20 0.82533377155766 0.349332456884679 0.174666228442339 21 0.85957515301341 0.280849693973181 0.140424846986590 22 0.901838957582494 0.196322084835012 0.0981610424175062 23 0.891719003465322 0.216561993069357 0.108280996534678 24 0.854461817925256 0.291076364149488 0.145538182074744 25 0.810003919741057 0.379992160517886 0.189996080258943 26 0.769894838917443 0.460210322165113 0.230105161082557 27 0.72546563819657 0.54906872360686 0.27453436180343 28 0.705345483107742 0.589309033784516 0.294654516892258 29 0.689026516418904 0.621946967162193 0.310973483581096 30 0.690977115916369 0.618045768167262 0.309022884083631 31 0.70825858731472 0.583482825370559 0.291741412685279 32 0.685048974999259 0.629902050001482 0.314951025000741 33 0.738514120677755 0.52297175864449 0.261485879322245 34 0.887074624440571 0.225850751118858 0.112925375559429 35 0.913173709542421 0.173652580915158 0.0868262904575789 36 0.90508996316513 0.189820073669742 0.0949100368348708 37 0.888573134711609 0.222853730576782 0.111426865288391 38 0.880490238509587 0.239019522980826 0.119509761490413 39 0.863903115395119 0.272193769209762 0.136096884604881 40 0.844261084949329 0.311477830101342 0.155738915050671 41 0.819447258963693 0.361105482072614 0.180552741036307 42 0.831823139787421 0.336353720425158 0.168176860212579 43 0.918860602073416 0.162278795853168 0.081139397926584 44 0.88350879555372 0.232982408892561 0.116491204446281 45 0.881136395976193 0.237727208047614 0.118863604023807 46 0.899553323117646 0.200893353764709 0.100446676882354 47 0.903740180228642 0.192519639542717 0.0962598197713583 48 0.871369905047184 0.257260189905631 0.128630094952816 49 0.85233319088547 0.29533361822906 0.14766680911453 50 0.863003630338801 0.273992739322398 0.136996369661199 51 0.883914261921166 0.232171476157668 0.116085738078834 52 0.847092662879812 0.305814674240377 0.152907337120188 53 0.795632365471529 0.408735269056942 0.204367634528471 54 0.734162990205253 0.531674019589493 0.265837009794747 55 0.979764426980249 0.0404711460395024 0.0202355730197512 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 3 0.0588235294117647 NOK 5% type I error level 4 0.0784313725490196 NOK 10% type I error level 4 0.0784313725490196 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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